In the modeling of complex dynamical systems, high-resolution finite element models are routinely adopted to reduce the discretization error. Such an approach may fail to enhance the confidence in simulation-based predictions when the dynamical systems exhibit significant variability in the parameterization and description of the mathematical model due to parametric (data) uncertainty and model uncertainty. In contrast to parametric uncertainty, model uncertainty poses significant challenges as no explicit parameter is available a priori to characterize its behavior. In the current investigation, a set of sprung-mass oscillators randomly attached to a baseline system (namely, a homogeneous cantilever plate) gives rise to model uncertainty. Contrary to model parametric uncertainty traditionally tackled using stochastic finite element method (SFEM), the model uncertainty arising from randomly attached sprung-masses gives rise to a new variant of dynamical system for every sample. The feasibility of adopting a Wishart random matrix to represent such ensemble of dynamical systems derived from model perturbation is investigated in this paper. The experiments conducted on a vibrating plate with randomly attached sprung-mass oscillators demonstrate that the Wishart random matrix model may provide a reasonable representation of model uncertainty in linear dynamical systems in the medium and high-frequency region.

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Journal Journal of Sound and Vibration
Adhikari, S. (S.), & Sarkar, A. (2009). Uncertainty in structural dynamics: Experimental validation of a Wishart random matrix model. Journal of Sound and Vibration, 323(3-5), 802–825. doi:10.1016/j.jsv.2009.01.030